The coefficient of apparent expansion of mercury in a glass vessel is `153xx10^(-6)//""^(@)C` and in a steel vessel is `144xx10^(-6)//""^(@)C`. If `alpha` for steel is `12xx10^(-6)//""^(@)C` then, that of glass is

Options

A. `9xx10^(-6)//""^(@)C`
B. `6xx10^(-6)//""^(@)C`
C. `36xx10^(-6)//""^(@)C`
D. `27xx10^(-6)//""^(@)C`

Explanation

To find the coefficient of linear expansion (α) for glass, we can use the relationship between the apparent expansion of mercury in different vessels and the coefficients of linear expansion of the materials of the vessels.

### Step-by-step Solution:

1. **Understand the relationship**: The coefficient of apparent expansion (γ) of a liquid in a vessel can be expressed as:
\[ \gamma = \gamma_{real} + \alpha_{vessel} \]
where:
- γ is the apparent expansion of the liquid,
- γ_{real} is the real expansion of the liquid (which is the same for both vessels),
- α_{vessel} is the coefficient of linear expansion of the vessel material.

2. **Set up the equations**: For the glass vessel and the steel vessel, we can write:
\[ \gamma_{glass} = \gamma_{real} + \alpha_{glass} \]
\[ \gamma_{steel} = \gamma_{real} + \alpha_{steel} \]

3. **Substituting known values**: We know:
- γ_{glass} = 153 × 10^(-6) °C^(-1)
- γ_{steel} = 144 × 10^(-6) °C^(-1)
- α_{steel} = 12 × 10^(-6) °C^(-1)

4. **Equating the two expressions for γ_{real}**:
From the steel vessel:
\[ \gamma_{real} = \gamma_{steel} - \alpha_{steel} \]
Substituting the known values:
\[ \gamma_{real} = 144 × 10^{-6} - 12 × 10^{-6} = 132 × 10^{-6} °C^{-1} \]

5. **Finding α_{glass}**: Now substitute γ_{real} back into the equation for the glass vessel:
\[ 153 × 10^{-6} = 132 × 10^{-6} + \alpha_{glass} \]
Rearranging gives:
\[ \alpha_{glass} = 153 × 10^{-6} - 132 × 10^{-6} = 21 × 10^{-6} °C^{-1} \]

6. **Final answer**: Therefore, the coefficient of linear expansion for glass is:
\[ \alpha_{glass} = 21 × 10^{-6} °C^{-1} \]